A satellite with a mass of ms = 7.00 × 103 kg is in a planet's equatorial plane in a circular "synchronous" orbit. This means that an observer at the equator will see the satellite being stationary overhead (see figure below). The planet has mass mp = 8.59 × 1025 kg and a day of length T = 1.1 earth days (1 earth day = 24 hours).
(a) How far from the center (in m) of the planet is the satellite?
(b) What is the escape velocity (in km/sec) of any object that is at the same distance from the center of the planet that you calculated in (a)?
set gravitation force equal to centripetal force
GMe*m/(r^2)=mwr where w=2PI/Period
so change T to seconds, solve for r
R=(G*mp*T^2/(4*pi^2))^(1/3)
Vesc=sqrt(2*mp*G/R)